Question # 1 (30 points)
Consider the following project network that corresponds to the activities required by a
new computer software product development and their precedence relationships.
The activity time estimates (in weeks) are as follows:
Activity Optimistic Most probable Pessimistic
A 3  3.5  7
B 3  4  5
C 2  3  4
D 4  5  6
E 4.5  6  7.5
F 7.5  8.5  12.5
G 6  10  14
H 4  5  6
I 2  3.5  6
J 5  6  13
K 5  8  12
A
Start
B
D
C
K
E
G
F
I
Finish
H
J
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(a) Determine the expected time and the variance of each activity (6 points).
(b) Find the critical path (3 points).
(c) What is the expected project completion time? What is its corresponding variance?
(3 points)
(d) Determine the probability that the project can be completed in less or equal than
29 weeks. (3 points)
(e) Suppose the management wants a 99% probability to complete the project in 29
weeks. If the variance in the project completion time is the same as in part (c),
what should be the expected project completion time? (3 points)
(f) Develop the linear programming models that can be used to determine the earliest
and the latest starting times of the project activities (do not solve). (12
points)

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